Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#2094 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C37 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C37 |
| prime radical | C22×D4×C37 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ C2×C42×C37 ◁ G | |
290 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(42,43,45,47)(44,48,49,46)(50,51,54,55,53,57,52,56);(38,39)(40,41)(42,44,45,49)(43,46,47,48)(51,55)(52,54)(56,57);(39,41)(51,55)(52,54)(56,57)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#7435, C37×#7822, C37×#7823, … |
| maximal normal subgroup of | C37×#7435, C37×#7822, C37×#7823, … |
| maximal quotient of | C37×#10661, C37×#10666, C37×#10672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 826);